Department of Pure Mathematics, Ferdowsi University of Mashhad (in cooperation with the Center of Excellence in Analysis on Algebraic Structures)Khayyam Journal of Mathematics2423-47889120230101On matrix-valued Gabor Bessel sequences and dual frames over locally compact abelian groups8910116447810.22034/kjm.2022.354990.2625ENLalitVashishtDepartment of Mathematics, Shivaji College,
University of Delhi, Delhi-110027, IndiaUttamSinhaDepartment of Mathematics, Shivaji College,
University of Delhi, Delhi-110027, India0000-0002-6028-9163Journal Article20220805We study matrix-valued Gabor Bessel sequences and frames in the matrix-valued space $L^2(G, \mathbb{C}^{n\times n})$, where $G$ is a locally compact abelian group and $n$ is a positive integer. Firstly, we show that the Bessel condition (or upper frame condition) can be extended from $L^2(G)$ to its associated matrix-valued signal space $L^2(G,\mathbb{C}^{n\times n})$, and conversely. However, this is not true for the lower frame condition. Secondly, we give sufficient conditions for the extension of a pair of matrix-valued Bessel sequences to matrix-valued dual frames over LCA groups. A special class of matrix-valued dual generators is given. It is shown that the symmetric windows associated with a given matrix-valued Gabor frames constitutes a Gabor frame in matrix-valued spaces over LCA groups.https://www.kjm-math.org/article_164478_4b32fc06a31389c74db8589382514098.pdf